We present a growth model in which investment in physical capital shows positive externalities which build up knowledge capital. A prerequisite for these spillovers to take place is that a country devotes time to education. Externalities associated with investment need education to raise the stock of knowledge capital. Analysing the competitive economy we demonstrate that the model may explain why some low-income countries show convergence whereas others do not. Furthermore, we demonstrate that in the social optimum the level of investment is always higher than in the competitive economy whereas the time spent for education may be lower or higher. We also show how the competitive economy may replicate the social optimum for an appropriate choice of a lump-sum tax and an investment subsidy. Empirical evidence is provided in order to demonstrate the plausibility of our model. (C) 2002 Elsevier Science B.V. All rights reserved.